Hardy–Weinberg equilibrium is a baseline model for judging whether a population is evolving. Two key conditions—very large population size and no migration—prevent chance and movement from shifting allele frequencies between generations.

Why these assumptions matter in Hardy–Weinberg

Hardy–Weinberg equilibrium describes an idealized population in which allele frequencies remain constant over time. The assumptions “large population” and “no migration” specifically eliminate two major causes of allele-frequency change that are not natural selection:

• random sampling effects from one generation to the next

• gene movement into or out of the population

Assumption 1: Very large population size

In a very large population, the alleles passed to the next generation are a more reliable “sample” of the current gene pool. This reduces random fluctuations in allele frequencies.

These allele-frequency trajectories show how genetic drift causes random, generation-to-generation fluctuations in allele frequency, with much stronger divergence among replicate populations when population size is small. In larger populations, replicate trajectories stay closer together over time, illustrating how random sampling effects “average out” as $N$ increases. Source

Genetic drift is always possible, but its impact becomes negligible as population size increases because:

• random deviations in who survives and reproduces tend to “average out”

• rare alleles are less likely to be lost purely by chance

• genotype frequencies are less likely to deviate from Hardy–Weinberg expectations due to sampling error alone

What “large” means in practice

“Large” is relative to the question being asked. For AP Biology, the key idea is qualitative:

• small populations show noticeable, unpredictable allele-frequency shifts across generations

• very large populations are much more stable unless other evolutionary forces act

Assumption 2: No migration (no gene flow)

Hardy–Weinberg also assumes the population is closed to the movement of alleles. If individuals enter or leave and successfully reproduce, they can add or remove alleles, changing allele frequencies.

This diagram illustrates gene flow as the movement of an individual from one population to another, followed by mating that transfers alleles into the recipient gene pool. By introducing alleles (or changing their frequencies), migration directly violates the Hardy–Weinberg assumption of no gene flow. Source

Gene flow violates Hardy–Weinberg because it directly alters the gene pool:

• immigration can introduce new alleles or increase the frequency of existing alleles

• emigration can remove alleles, especially if the departing individuals are not genetically representative of the population

Important nuance: migration must affect reproduction

Movement alone is not enough to break the assumption. Hardy–Weinberg is disrupted when migrants contribute genes to the next generation (or when emigrants would have contributed but are removed).

How violating these assumptions changes allele frequencies

When either assumption is violated, allele frequencies can change even if no trait is being “selected.”

If population size is not large

• allele frequencies can drift upward or downward by chance

• drift can reduce genetic variation within the population over time, especially for rare alleles

• different small populations can diverge from each other simply due to random changes

If migration occurs

• allele frequencies can shift toward the allele frequencies of the source population(s)

• gene flow can increase genetic variation within the receiving population by adding alleles

• repeated gene flow can make separate populations more genetically similar

Interpreting real populations using these assumptions

When comparing observed genotype frequencies to Hardy–Weinberg expectations, keep these interpretation cues in mind:

• Unpredictable, generation-to-generation allele-frequency changes are consistent with non-large population effects (drift).

• Directional allele-frequency shifts that match known movement between populations are consistent with migration/gene flow.

• If both small population size and migration are plausible, both can contribute; Hardy–Weinberg is a null model, so any failed assumption can explain deviations.